论文标题
基于能量的潜在变量模型中得分函数的变分（梯度）估计值
Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models
论文作者
论文摘要
没有任何结构假设的基于能量的潜在变量模型（EBLVM）的学习和评估是高度挑战性的，因为真正的后代和分区在此类模型中的功能通常是棘手的。本文介绍了分数函数及其梯度相对于一般EBLVM中的模型参数的变异估计，分别称为VAE和VAGE。训练变异后验，以最大程度地减少对真实模型后部的一定差异，并且两个估计值中的偏差都可以通过理论上的差异来界定。通过最小的模型假设，可以将VAE和VAGE应用于内核化的Stein差异（KSD）和得分匹配（SM）基于学习EBLVM的方法。此外，VAE还可以用来估计数据和一般EBLVM之间的确切的Fisher差异。
The learning and evaluation of energy-based latent variable models (EBLVMs) without any structural assumptions are highly challenging, because the true posteriors and the partition functions in such models are generally intractable. This paper presents variational estimates of the score function and its gradient with respect to the model parameters in a general EBLVM, referred to as VaES and VaGES respectively. The variational posterior is trained to minimize a certain divergence to the true model posterior and the bias in both estimates can be bounded by the divergence theoretically. With a minimal model assumption, VaES and VaGES can be applied to the kernelized Stein discrepancy (KSD) and score matching (SM)-based methods to learn EBLVMs. Besides, VaES can also be used to estimate the exact Fisher divergence between the data and general EBLVMs.
